Stochastic Analysis meets QFT - critical theory

Over the last years, a number of new methods from stochastic analysis have been developed that allowed a new perspective on constructive field theory. Among these are the theory of singular stochastic PDEs, Barashkov-Gubinelli’s variational approach, and constructive approaches to Polchinski's continuous renormalisation group flow. While much progress has been made on controlling small scales for subcritical/superrenormalisable models there is much less known regarding the same question  for critical/just-renormalizable models.

The constructive renormalisation programme has been successfully applied to quantum field theories of matrix models and tensor models. Matrix models tend to be asymptotically safe and tensor models asymptotically free at their critical dimension. These models are comparably simple and thus provide an ideal target to extend the above stochastic analysis methods to critical dimension.

The aim of this short workshop is to bring together some leading experts from both the stochastic analysis community and the QFT community to explore these exciting developments further.